The D7000 (like other Nikon DSLR's) does not turn itself off altogether. It does have a configurable delay that controls when the rear monitor display goes off when viewing the menus or an image - this is on page 215 in the camera manual - Custom Setting c4 Monitor off Delay. There is also a setting that controls how long the camera meter and the top LCD display stay active - page 214 Custom Setting c2 Auto Meter-off Delay.
I'm sorry you've had problems with your camera, but contrary to what you may have read elsewhere, there has been no "notorious" oil-splatter issue on the D7000, and not really any consistent "back-focus" problem or general faults with genuine MB-D11 battery grips either. Many of the early complaints about poor sharpness proved to be down to a lack of technique or understanding on the part of the photographer, though to be fair there were a few credible reports of focus faults with the camera.
Now that you have found Nikonians, hopefully we will be able to help you identify what are real problems and suggest ways of resolving them